Q1: Do I gain 2 memory for this card’s Start of Your Turn effect if both me and my opponent have 8 or more cards in hand?
Yes, you gain 2 memory if both of the conditions are met.
Q2: Can I also activate this card’s Your Turn effect when one of my blue or red Digimon becomes unsuspended during the unsuspend phase?
Yes, you can.
Matt Ishida & Sora Takenouchi BT9-085 R [Start of Your Main Phase] If you have 8 or more cards in hand, gain 1 memory. If your opponent has 8 or more cards in hand, gain 1 memory. [Your Turn] When one of your blue or red Digimon becomes unsuspended, you may suspend this Tamer to return 1 of your opponent's level 3 Digimon to its owner's hand. --- [Security] Play this card without paying its memory cost.
Matt Ishida & Sora Takenouchi BT9-085 R [Start of Your Main Phase] If you have 8 or more cards in hand, gain 1 memory. If your opponent has 8 or more cards in hand, gain 1 memory. [Your Turn] When one of your blue or red Digimon becomes unsuspended, you may suspend this Tamer to return 1 of your opponent's level 3 Digimon to its owner's hand. --- [Security] Play this card without paying its memory cost.
Matt Ishida & Sora Takenouchi BT9-085 R [Start of Your Main Phase] If you have 8 or more cards in hand, gain 1 memory. If your opponent has 8 or more cards in hand, gain 1 memory. [Your Turn] When one of your {{Colour|blue}} or {{Colour|red}} Digimon becomes unsuspended, you may suspend this Tamer to return 1 of your opponent's level 3 Digimon to its owner's hand. ---
石田ヤマト&武之内空 BT9-085 R 【自分のメインフェイズ開始時】自分の手札が8枚以上のとき、メモリー+1。相手の手札が8枚以上のとき、メモリー+1。【自分のターン】青か赤の自分のデジモンがアクティブになったとき、このテイマーをレストさせることで、Lv.3の相手のデジモン1体を手札に戻す。 --- 【セキュリティ】このカードをコストを支払わずに登場させる。